Two New Predictor-Corrector Iterative Methods with Third- and Ninth-Order Convergence for Solving Nonlinear Equations

In this paper, we suggest and analyze two new predictor-corrector iterative methods with third and ninth-order convergence for solving nonlinear equations. The first method is a development of [M. A. Noor, K. I. Noor and K. Aftab, Some New Iterative Methods for Solving Nonlinear Equations, World Applied Science Journal, 20(6),(2012):870-874.] based on the trapezoidal integration rule and the centroid mean. The second method is an improvement of the first new proposed method by using the technique of updating the solution. The order of convergence and corresponding error equations of new proposed methods are proved. Several numerical examples are given to illustrate the efficiency and performance of these new methods and compared them with the Newton's method and other relevant iterative methods. Keywords: Nonlinear equations, Predictor–corrector methods, Trapezoidal integral rule, Centroid mean, Technique of updating the solution; Order of convergence

Integrated optical components for quantum key distribution

The security of current public key cryptosystems, such as RSA, depends on the difficulty of computing certain functions known as trapdoor functions. However, as computational resources become more abundant with the fast development of super- and quantum computers, relying on such methods for communication security becomes risky. Quantum key distribution (QKD), is a potential solution that can allow theoretically secure key exchange for future communications. Chip-scale integration of this solution for securing communication of embedded systems and hand held devices demands miniaturizing the optical components that are used in typical QKD boxes, hence reducing its size and cost. The aim of the work in this thesis is firstly investigating novel approaches to realising integrable single photon sources and detectors for applications such as QKD, and secondly proposing a chip-scale integrated QKD system with efficient and optimised optical components. In the first part of the thesis, a model for coupling 2D material emitters to rod-type photonic cavities is studied for room temperature single photon sources. Our investigated approach allows better coupling between the emitter and the cavity modes than conventional methods, while increasing light collection ratio. In the second part, site-controlled growth of semiconductor III-V nanowires on Si for photodetection applications is achieved by fabricating the sites using electron-beam lithography and wet etching. Studies were also carried out to investigate the effect of the wafer’s growth temperature on the nanowire formation. Finally, a model was proposed for realising a chip-scale QKD system using photonic crystals as a photonic circuit platform. The work involves increasing the Q-factor of the cavity single photon source, increasing cavity waveguide coupling, reducing losses in beam splitters and out-couplers. A final model of a chip-scale QKD system which involves the optimised components is proposed at the end of the thesis

On the Remes Algorithm for Rational Approximations

This paper is concerned with the minimax approximation of a discrete data set by rational functions. The second algorithm of Remes is applied. A crucial stage of this algorithm is solving the nonlinear system of leveling equations. In this paper, we will give a new approach for this purpose. In this approach, no initial guesses are required. Illustrative numerical example is presented

Increasing Light Absorption and Collection Using Engineered Structures

In recent years we have witnessed an explosion of interest in two dimensional (2D) materials, due to their unique physical properties. Excitement surrounds the promise of replacing conventional bulk photodetectors with devices based on 2D materials, allowing better integration, flexibility and potentially improving performance. However, the low inherent light absorption of 2D materials is an outstanding issue to be solved. In this chapter we review two independent approaches to tackling this problem, which have the potential to be combined to find a robust solution. The first approach involves patterning the substrate with a rod-type photonic crystal (PhC) cavity structure, which is shown to increase the light absorption into a 2D material flake coupled spatially to the cavity mode. Secondly, we review 2D–compatible solid immersion lenses (SILs) and their ability to increase both the optical magnification of the structures they encapsulate, and the longevity of the material. SILs have been shown to reduce the requirements for complex optics in the implementation of 2D materials in optoelectronic devices, and also in preserving the photodetector’s optical performance over long periods of time. Finally, we show how by combining rod-type PhC cavities with SILs, we can improve the performance of 2D material-based photodetectors

The Role of Financial Literacy in Achieving Financial Satisfaction Through Financial Well-Being

Purpose:  The aim of this study is to identifying the financial knowledge's role in the achievement of financial satisfaction through financial well-being.   Theoretical framework: The financial service sector in Iraq has been undergoing major transformation due to technological developments and innovations in terms of operating efficiency, This requires increasing financial knowledge of customers to use financial technology.   Design/Methodology/Approach: The Employees working in public sector and workers working in private sectors were taken as the study sample, for identifying the differences among them at the level of dimensions and research variables, A total of (360) valid questionnaires were collected for statistical analysis after the survey was distributed electronically. Three hypotheses were examined in the study using a statistical program (SMART PLS) to determine whether there was a correlation and influence among the variables of the study.   Findings: The results study proves that the workers' financial satisfaction in private sector is better than the financial satisfaction of workers in public sector due to employees’ feeling of salary threat as a result of the political unrest.   Research, practical and social implications: The study Due to the political unrest in Iraq, government departments must consider employee satisfaction by providing financial compensation and by maintaining their pay without being compromised.   Originality/Value: The value of the study recommends the needs to increase the awareness and knowledge Financial and conduct future studies could concentrate on concrete, feasible strategies that management might use to enhance workers' financial well-being in line with the recommendations of this study

Nanowires for Room-Temperature Mid-Infrared Emission

InAs-based nanowires hold a promise to offer transformational technologies for infrared photonic applications. Site-controlled InAs nanowire growth on low-cost Si substrates offers the practical integration advantages that silicon photonics benefits from. This includes the realisation of cheap photonic circuitries, light emitters and detectors that are otherwise expensive to realise with III/V material-based substrates. This chapter details the growth development of advanced faceted multi-quantum well structures within InAs nanowires using molecular beam epitaxy. We review the crystal structure for the faceted quantum wells along with an analysis of their optical emission characteristics which shows quantum confinement and localisation of the carriers on the quantum well nanostructure. This enables tuning of the emission wavelength and enhanced emission intensity up to the technologically important room-temperature operation point

Increasing the extraction efficiency of quantum light from 2D materials

Direct bandgap 2D semiconductor materials such as monolayers of transition metal dichalcogenides (TMDCs), show great promise in optoelectronic devices enabling exciting new technologies such as ultra-thin quantum light LED’s [1]. These structures can have incredible advantages, enabling almost seamless integration into conventional silicon structures. However, extracting light out of these structures can be a challenge, often requiring costly and time consuming processing e.g. engineered waveguides or cavities [2]. Furthermore none of these methods allow you to observe the light directly, therefore are unhelpful in certain applications, such as an optical version of a quantum unique device [3]. We have previously demonstrated that epoxy based solid immersion lenses can be used to increase light out of semiconductor nanostructures. We furthered this idea to see if they could be used to increase the light out of monolayer TMDC materials; and investigate how the epoxy-2D material interface affects the emission. Our studies revealed that a SIL can greatly enhance the photoluminescence of WSe2 by up to 6x (more than theory predicts for a SIL of this shape), without effecting the wavelength (figure 1). However we also found that the epoxy appears to reduce the emission of the MoS2, suggesting that there could be doping effects due to the epoxy. Overall this method shows great promise as a cheap, and scalable method for enhancing the efficiency of low intensity WSe2 based devices

Photonic crystals for enhanced light extraction from 2D materials

In recent years, a range of two-dimensional (2D) transition metal dichalcogenides (TMDs) have been studied, and remarkable optical and electronic characteristics have been demonstrated. Furthermore, the weak interlayer Van der Waals interaction allows TMDs to adapt to a range of substrates. Unfortunately, the photons emitted from these TMD monolayers are difficult to efficiently collect into simple optics, reducing the practicality of these materials. The realization of on-chip optical devices for quantum information applications requires structures that maximize optical extraction efficiently whilst also minimizing substrate loss. In this work we propose a photonic crystal cavity based on silicon rods that allows maximal spatial and spectral coupling between TMD monolayers and the cavity mode. Finite difference time domain (FDTD) simulations revealed that TMDs coupled to this type of cavity have highly directional emission towards the collection optics, as well as up to 400% enhancement in luminescence intensity, compared to monolayers on flat substrates. We consider realistic fabrication tolerances and discuss the extent of the achievable spatial alignment with the cavity mode field maxima

Increasing quantum light extraction from TMDC's

Much of the recent explosion of research into 2D semiconductor materials has focused on direct bandgap materials such as monolayers of transition metal dichalcogenides (TMDCs), which show great promise in optoelectronic devices such as ultra-thin LEDs [1, 2]. Extraction of light out of these structures can be enhanced in the near field through the integration of these monolayers into waveguides, cavities, or photonic crystals [3]; however these methods are not ideal as they require costly and time consuming processing. Furthermore none of these methods allow you to observe the light directly, therefore are unhelpful in certain applications, such as quantum unique devices [4]. The research we present demonstrates a solution to this problem by encapsulating a range of two-dimensional materials in Solid Immersion Lenses (SILs), dynamically-shaped from UV cure epoxy. We show that the advantages of using SILs formed in this way are numerous, with the most prominent being they can be deterministically placed and directly tuned, to ensure the extraction efficiency is maximised. We will also present detailed photoluminescence maps showing how the reduction of laser spot size caused by focusing through a SIL can allow for very detailed mapping of WSe2 multilayer structures